
Challenges and Contributions.
Numerous applications of the shortest cycle counting, particularly in online situations, demand real-time response to the query [1]}, [2]}. Thus, it is critical to develop a real-time algorithm capable of counting the shortest cycles. A straightforward solution is to calculate the number of shortest cycles for each vertex in advance and record the values. Then, any query can be answered with \(O(1)\)  time complexity. Nevertheless, such a simple approach cannot handle dynamic graphs well since it requires to re-compute the shortest cycles for all vertices regarding graph updates. This is because of the lack of awareness for distance information among vertices within the graph.
Hence, it is challenging to build an index that supports both real-time query answering and fast updates in the face of dynamic changes.
